The Quantum Mechanical Model Work to relate wave behavior, atomic energy levels, and electrons by Louis deBroglie and Erwin Schrodinger led to the branch of physics called quantum mechanics. Quantum mechanics and probability, the statistical likelihood of an occurrence, are the basis for current atomic models. Electrons are particles with wave characteristics. Probability helps describe the behaviors and positions of electrons. One important assumption of today’s model is the Heisenberg Uncertainty Principle which states that it is not possible to describe both position and speed of an electron at the same point in time.

The Quantum Mechanical Model An important distinction to make is that between an orbit (a pathway, as in Bohr’s Model of the atom) and an orbital. An orbital is a region of space around a nucleus in which an electron is most likely to be found. It is not a barrier or pathway, only a model describing the likely occupied area.

The Quantum Mechanical Model Schrodinger developed a mathematical model for the wave behavior of an electron. The very complex equation contains four quantum numbers that are used to describe electron location and behavior…

The Quantum Mechanical Model

The Quantum Mechanical Model n Principle Quantum Number refers to the energy level location of the electron n is 1,2,3,4,… n (up to 7) the number of sublevels in the energy level = n (up to 4) the number of available orbitals in the energy level = n2 (up to 16) the greatest number of electrons contained in any one energy level = 2n2 (up to 32). Ex: where n=3, the maximum number of electrons is 2(3)2 = 18.

The Quantum Mechanical Model l  Azimuthal or Orbital Quantum Number refers to the sublevel location of the electron l is either s, p, d, or f s= 0, p=1, d=2, f=3 s-sublevel orbitals are spherical in shape. They are closest to the nucleus; thus electrons located here have the lowest relative energies within the energy level. There is only 1 s-orbital per energy level.

The Quantum Mechanical Model p-sublevel orbitals are dumbbell-shaped. They are a little farther from the nucleus; thus electrons located here have a little higher relative energies within the energy level. There are 3 p-orbitals (px, py, pz) per energy level, starting with energy level 2.

The Quantum Mechanical Model d-sublevel orbitals are cloverleaf-shaped, very complex. They are even a little farther from the nucleus; thus electrons located here have even higher relative energies within the energy level. There are 5 d-orbitals per energy level, starting with energy level 3.

The Quantum Mechanical Model f-sublevel orbitals are extremely complex in shape. They are farthest from the nucleus; thus electrons located here have the highest relative energies within the energy level. There are 7 f-orbitals per energy level, starting with energy level 4.

The Quantum Mechanical Model ml Magnetic Quantum Number designates the number of orbitals on each sublevel and in which specific orbital the electron is likely located describes the home orbital’s geometric orientation about the x, y, and z axes Ex if l is 1 (in p orbital) ml could be (-1, 0 or 1) (x, y, or z plane) ml= (-l to l) including 0

The Quantum Mechanical Model ms  Spin Quantum Number describes the direction of spin for the electron ms is either +1/2 (clockwise spin) or –1/2 (counter- clockwise spin). The Pauli Exclusion Principle is very important here and throughout the quantum model. It states that: 1) no more than 2 electrons may occupy any one orbital; 2) if electrons occupy the same orbital, they must have opposite spin directions; 3) thus, no two electrons in one atom will have all four quantum numbers identical.

The Quantum Mechanical Model ms is either +1/2 (clockwise spin) or –1/2 (counter-clockwise spin) The Pauli Exclusion Principle 3p____ _______ _______ X no more than 2 electrons may occupy any one orbital 3p _____ _____ ________ if electrons occupy the same orbital, they must have opposite spin directions; 3p _____ _____ ________ X

Orbital Diagrams & Electron Configurations There are 3 basic rules that govern orbital filling: Aufbau Principle – electrons enter lowest energy levels first. Hund’s Rule – when electrons fill orbitals within a sublevel, each orbital is occupied by one electron before any orbital obtains two electrons. All electrons in singly occupied orbitals have the same spin directions. Pauli Exclusion Principle – described earlier